The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 sider |
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Side 77
... pass through it . Therefore , if two circles , & c . Q. E. D. PROP . XII . THEOR . IF two circles touch each other externally , the straight line which joins their centres shall pass through the point of contact . Let the two circles ...
... pass through it . Therefore , if two circles , & c . Q. E. D. PROP . XII . THEOR . IF two circles touch each other externally , the straight line which joins their centres shall pass through the point of contact . Let the two circles ...
Side 78
... pass otherwise than through the point of contact A , that is , it must pass through it . Therefore , if two circles , & c . Q. E. D. See N. PROP . XIII . THEOR . ONE circle cannot touch another in more points than one , whether it ...
... pass otherwise than through the point of contact A , that is , it must pass through it . Therefore , if two circles , & c . Q. E. D. See N. PROP . XIII . THEOR . ONE circle cannot touch another in more points than one , whether it ...
Side 79
... passing through the centre , cuts the straight line AB , which does not pass through the centre , åt right angles , it also bisects it : wherefore AF is equal to FB , and AB double of AF . For the same reason , CD is double of CG : and ...
... passing through the centre , cuts the straight line AB , which does not pass through the centre , åt right angles , it also bisects it : wherefore AF is equal to FB , and AB double of AF . For the same reason , CD is double of CG : and ...
Side 82
... passes between H B A D that straight line and the perpendicular AE . And this is all ' that is to be understood , when , in the Greek text and transla- ' tions from it , the angle of the semicircle is said to be greater ' than any acute ...
... passes between H B A D that straight line and the perpendicular AE . And this is all ' that is to be understood , when , in the Greek text and transla- ' tions from it , the angle of the semicircle is said to be greater ' than any acute ...
Side 88
... pass through the other points ; and the circle of which ABC is a segment is described : and because the centre D is in AC , the segment ABC is a se- d 9.3 . B B D B 444 E C D A E D micircle but if the angles ABD , BAD are not equal to ...
... pass through the other points ; and the circle of which ABC is a segment is described : and because the centre D is in AC , the segment ABC is a se- d 9.3 . B B D B 444 E C D A E D micircle but if the angles ABD , BAD are not equal to ...
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram perpendicular point F polygon prisms proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure right angles segment sides BA similar sine solid angle solid parallelepipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 30 - Any two sides of a triangle are together greater than the third side.
Side 64 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Side 30 - IF, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let...
Side 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 165 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Side 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.
Side 39 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Side 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.